You can either click the search button at the top of main screen and enter the game id or load someone's profile and view their match history. To get to your own profile click your name at the top right, to get to someone else's either double click the rankings or search in the same way you found the game by id. Searching for names should be done with correct casing.

I would prefer if the match could be played back at once, like with testSnapcam();, but without the auto-panning and -zooming.

Or can I suggest making the camera changes smoother and slower, e.g. if a unit at the edge of the map dies and the remaining units are far away, the zoom-in on the remaining units shouldn't be so fast. And if a unit runs away from the rest (increasing the area that needs to be covered by the camera) the camera should already have started zooming out before that unit starts to run, so it'll be smoother and easier to watch.

If that can be done then it might also be good to have an option for changing how much smoothing is applied to the camera changes. More smoothing would mean that the game has to look further ahead in time and compute the camera's f-curves from all the units' movements—which could probably become too CPU-intensive if that look-ahead time exceeds a certain length (varying between different hardware configurations of course), so the maximum smoothing amount would have to be capped at a limit, or it would get pretty un-smooth...

More padding between the outermost units and the screen edges would be better in my opinion as well (and making that an adjustable setting would again be cool—so everyone can customize it and watch matches in the way that is most comfortable or exciting to them).